The fossil from an extinct Carcharocles megalodon - which lived more than three million years ago and is believed to have grown up to 15 metres in length - was discovered by the veteran broadcaster furing a family holiday on the island in the late 1960s.
Mr Attenborough, 94, presented the tooth to the seven-year-old prince after a private viewing of his new documentary at Kensington Palace. George appeared intrigued at the gift in a photograph issued by the royal family.
However Malta's culture minister Jose Herrera said he wanted to "get the ball rolling" on returning the artifact to his nation's heritage collection.
Mr Herrera told the Times of Malta: There are some artifacts that are important to Maltese natural heritage and which ended up abroad and deserve to be retrieved,” Herrera said.
"We rightly give a lot of attention to historical and artistic artifacts. However, it is not always the case with our natural history. I am determined to direct a change in this attitude."
The removal or excavation of "object of geological importance" has been banned in Malta since the since the Cultural Heritage Act came into force in 2002.
However Maltese MEP Roberta Metsola criticised the Mr Herrera's comments and suggested the government should focus on addressing the corruption allegations which have plagued the country since the murder of journalist Daphne Caruana Galizia in 2017.
"This is not satire," she tweeted. "We have lost the plot. Rather than fight to get back the millions it allowed to be stolen in corruption, this Malta government's priority is now to engage in a battle with a little boy for a shark's tooth given to him by the world's leading natural historian."
Ms Caruna Galizia's son Matthew added: "A megalodon tooth costs $40 on eBay. Corruption has cost us billions of euros. I ask my government to prioritise and please get a grip on what's important."
Kensington Palace declined to comment.
Additional reporting by agencies